Nonquadratic Lyapunov functions for robust control
Automatica (Journal of IFAC)
Piecewise Lyapunov functions for robust stability of linear time-varying systems
Systems & Control Letters
Automatica (Journal of IFAC)
Stability analysis of uncertain genetic sum regulatory networks
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Brief paper: Set invariance and performance analysis of linear systems via truncated ellipsoids
Automatica (Journal of IFAC)
Visual servoing path planning via homogeneous forms and LMI optimizations
IEEE Transactions on Robotics
Convex relaxations in circuits, systems, and control
IEEE Circuits and Systems Magazine
Analysis of linear systems using truncated ellipsoids
ACC'09 Proceedings of the 2009 conference on American Control Conference
International Journal of Systems Science - Dynamics Analysis of Gene Regulatory Networks
IEEE Transactions on Fuzzy Systems
Technical communique: LMI conditions for time-varying uncertain systems can be non-conservative
Automatica (Journal of IFAC)
Lyapunov characterization of forced oscillations
Automatica (Journal of IFAC)
Conjugate Lyapunov functions for saturated linear systems
Automatica (Journal of IFAC)
A Convex Condition for Robust Stability Analysis via Polyhedral Lyapunov Functions
SIAM Journal on Control and Optimization
Hi-index | 22.16 |
The problem addressed in this paper is the construction of homogeneous polynomial Lyapunov functions (HPLFs) for linear systems with time-varying structured uncertainties. A sufficient condition for the existence of an HPLF of given degree is formulated in terms of a linear matrix inequalities (LMI) feasibility problem. This condition turns out to be also necessary in some cases depending on the dimension of the system and the degree of the Lyapunov function. The maximum @?"~ norm of the parametric uncertainty for which there exists a homogeneous polynomial Lyapunov function is computed by solving a generalized eigenvalue problem. The construction of such Lyapunov functions is efficiently performed by means of popular convex optimization tools for the solution of problems in LMI form. Comparisons with other classes of Lyapunov functions through numerical examples taken from the literature show that HPLFs are a powerful tool for robustness analysis.